Data.Generics.Fixplate.Traversals

Uniplate-style traversals.

Toy example: Consider our favourite data type

data Expr e 
  = Kst Int 
  | Var String 
  | Add e e 
  deriving (Eq,Show,Functor,Foldable,Traversable)

instance ShowF Expr where showsPrecF = showsPrec

and write a function simplifying additions with zero:

simplifyAdd :: Mu Expr -> Mu Expr
simplifyAdd = transform worker where
  worker expr = case expr of
    Fix (Add x (Fix (Kst 0))) -> x    -- 0+x = x
    Fix (Add (Fix (Kst 0)) y) -> y    -- x+0 = 0
    _ -> expr

Unfortunately, all these Fix wrappers are rather ugly; but they are straightforward to put in, and in principle one could use Template Haskell quasi-quotation to generate patterns.

Queries

children :: Foldable f => Mu f -> [Mu f]

The list of direct descendants.

universe :: Foldable f => Mu f -> [Mu f]

The list of all substructures. Together with list-comprehension syntax this is a powerful query tool. For example the following is how you get the list of all variable names in an expression:

variables expr = [ s | Fix (Var s) <- universe expr ]

Traversals

transform :: Functor f => (Mu f -> Mu f) -> Mu f -> Mu f

Bottom-up transformation.

transformM :: (Traversable f, Monad m) => (Mu f -> m (Mu f)) -> Mu f -> m (Mu f)

topDownTransform :: Functor f => (Mu f -> Mu f) -> Mu f -> Mu f

Top-down transformation. This provided only for completeness; usually, it is transform what you want use instead.

topDownTransformM :: (Traversable f, Monad m) => (Mu f -> m (Mu f)) -> Mu f -> m (Mu f)

descend :: Functor f => (Mu f -> Mu f) -> Mu f -> Mu f

Non-recursive top-down transformation. This is basically just fmap.

descendM :: (Traversable f, Monad m) => (Mu f -> m (Mu f)) -> Mu f -> m (Mu f)

Similarly, this is basically just mapM.

rewrite :: Functor f => (Mu f -> Maybe (Mu f)) -> Mu f -> Mu f

Bottom-up transformation until a normal form is reached.

rewriteM :: (Traversable f, Monad m) => (Mu f -> m (Maybe (Mu f))) -> Mu f -> m (Mu f)

Structure change

restructure :: Functor f => (f (Mu g) -> g (Mu g)) -> Mu f -> Mu g

Bottom-up transformation (typically "shallow", that is, restricted to a single level) which can change the structure functor (actually transform is a special case of this).

restructureM :: (Traversable f, Monad m) => (f (Mu g) -> m (g (Mu g))) -> Mu f -> m (Mu g)

Context

context :: Traversable f => Mu f -> Attr f (Mu f -> Mu f)

We annotate the nodes of the tree with functions which replace that particular subtree.

contextList :: Traversable f => Mu f -> [(Mu f, Mu f -> Mu f)]

Flattened version of context.

Folds

foldLeft :: Foldable f => (a -> Mu f -> a) -> a -> Mu f -> a

(Strict) left fold. Since Mu f is not a functor, but a data type, we cannot make it an instance of the Foldable type class.

foldLeftLazy :: Foldable f => (a -> Mu f -> a) -> a -> Mu f -> a

foldRight :: Foldable f => (Mu f -> a -> a) -> a -> Mu f -> a